Production mix problem help

Quiz 9: Calculation of Production Mix 

Hours 

Reactor A 

Reactor B 

Product 1 

5 

3 

Product 2 

3 

3 

Product 3 

3 

4 

The table shows how many hours it takes reactors A and B to produce a ton of each 

product. From the table we see that for every ton of product 1 produced we need to 

run Reactor A for 5 hours and also run Reactor B for 3 hours. The two reactors are 

available for 40 hours and 30 hours per week respectively. We can determine the 

amount (in tons) of product 1, p 1 , product 2, p 2 , and product 3, p 3 that can be 

produced in a week using the following equations: 

5 p 1 + 3 p 2 + 3 p 3 = 40 

3 p 1 + 3 p 2 + 4 p 3 = 30 

Let F 1 , F 2 , F 3 represent the profit for a ton of each product . So the total weekly 

profit is given by: 

Profit = F 1 p 1 + F 2 p 2 + F 3 p 3 

Create a script M-file that uses the reduced row echelon function rref to solve for p 1 

and p 2 as functions of p 3 , and generates two subplots. The first subplot should show 

the total weekly profit as a function of p 3 for the following two cases: 

Case 1: F 1 = $400, F 2 = $600, F 3 = $100 

Case 2: F 1 = $600, F 2 = $200, F 3 = $200 

The second subplot shows p 1 and p 2 as a function of p 3 . 

Based on the results of the first subplot, your production manager says that she is 

going to adopt an all or nothing strategy on the production volume of product 3. She 

says that the plant will either produce the maximum amount of product 3 or none at 

all. What is her justification for this?

This is what I have so far. My second subplot looks wierd.

A=[5 3; 3 3];
b=[40- 3*p3; 30-4*p3];
p=A\b;

f1=400; f2=600; f3=100;
p3=[0:0.1:40];
P=f1*p(1)+f2*p(2)+f3*p3;
subplot(1,2,1)
plot(p3, P)
hold on
f1=600; f2=200; f3=200;
P=f1*p(1)+f2*p(2)+f3*p3;
plot(p3, P)

subplot(1,2,2)
plot(p(1),p3)
hold on
plot(p(2),p3)

Any suggestion is appreciated. Thanks!